If each side of a square is increased by 25%, find the percentage change in its area.

Q: If each side of a square is increased by 25%, find the percentage change in its area.

Let each side of the square be a. Then, area = . a 2 New side = 125 a 100 = 5 a 4 . New area = 5 a 4 2 = 25 a 2 16 Increase in area = 25 a 2 16 - a 2 = 9 a 2 16 Increase% = 9 a 2 16 * 1 a 2 * 100 % = 56.25%.

56.25%
36.25%
16.25%
12.25%

Correct Answer: 56.25%

Explanation:

Let each side of the square be a. Then, area = . $a 2$
New side = $\frac{125 a}{100} = \frac{5 a}{4}$ . New area = $\frac{5 a}{4} 2$ = $\frac{25 a 2}{16}$

Increase in area = $\frac{25 a 2}{16} - a 2 = \frac{9 a 2}{16}$
Increase% = $\frac{9 a 2}{16} * \frac{1}{a} * 100$ % = 56.25%.

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